4 Answers
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For malicious (really any) data to modify your computer, it is required that the data is interpreted at the target location. The only scenario I can see - and it is a far fetched one - is that some "smart socket" that may perform some action based on the quality or fluctuation on the network. Say that you, as an attacker, force the power fluctuation to perform the fluctuation-action, you can call this malicious activity. Far fetched.

Edit: As smart phones' charge connectors double as communication points, changing the roles is easy. If the phone charges from a computer, i.e. through USB, sending data instead is probably trivial. Of course, again, it's important that the phone interprets and acts on the incoming data.

Yes, it is possible, but not in the way you think. There exists a commercial and popular technology that enables you to have LAN (local network) over power lines in your house or business. Technology is called https://en.wikipedia.org/wiki/HomePlug. Its product (similar to a single socket surge protector) is plugged into an electric socket and it has an Ethernet port (computer network socket) into which you connect your computer. You need at least 2 such devices in your house (one for each networked device). According to my knowledge, this is the only possible way that you can infected with malware over a power line. Also, what "Henning Klevjer" said in his answer is also correct.

Unless you're all using ethernet-over-powerline technology such as HomePlug, I'd say it's highly unlikely. Your system has to actually interpret any data sent to it, which it shouldn't do unless it's designed to.

On a laptop, your power cable contains a switched-mode supply that regulates a DC voltage supply from the AC voltage supplied by your mains. This means that any signal or noise on the mains line is destroyed before it even reaches the laptop. The same type of supply is used on desktop machines. Even if an attacker generated large amounts of noise on the power line, the regulators in your power supply would entirely remove it, or shut down to protect your system.

If you've been infected, I'd guess you caught the malware over their network instead. If you connect to their wireless network, the malware on their machines might attempt to exploit various vulnerabilities on your system via the network. This can be mitigated by enabling your firewall, installing all OS and software updates, and limiting access to any network shares you provide.